For the last few years, I've only worked out first thing - for me, it's the only way I have no excuses, plus it really wakes me up and I have so much more energy all day than if I skip it. I haven't got back into running that early just yet, as it's still dark here until around 6am, but in the summer, it's really the only time I can workout outside - and even then it's already well into the 90's. Right now I get up at 5am and either head to the gym - mine is 24 hours - or to the new pool that just opened near me, which opens at 5am. As
Courtnie mentioned above, the hardest part is getting up - once I am physically out of bed, it's all downhill from there! I also am usually in bed by 9pm and for sure no later than 10pm, but my body has adjusted to that nicely. Even on weekends, I'm wide awake without an alarm by 6am, which is good because then I can go ride my horse before it's 110+ and it's just too hot to function.
My suggestions are to try it and stick with it for a few weeks - let your body get used to the changes. But also please be very cautious if you are running in the dark or a remote area - wear reflective clothing and run against traffic, if there is any. Always safety first!